Question: Simplify; express your answer in exponential form. Assume $p\neq 0, r\neq 0$. $\dfrac{{(p^{5})^{-3}}}{{(p^{5}r)^{-3}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{5}}$ to the exponent ${-3}$ . Now ${5 \times -3 = -15}$ , so ${(p^{5})^{-3} = p^{-15}}$ In the denominator, we can use the distributive property of exponents. ${(p^{5}r)^{-3} = (p^{5})^{-3}(r)^{-3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(p^{5})^{-3}}}{{(p^{5}r)^{-3}}} = \dfrac{{p^{-15}}}{{p^{-15}r^{-3}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{-15}}}{{p^{-15}r^{-3}}} = \dfrac{{p^{-15}}}{{p^{-15}}} \cdot \dfrac{{1}}{{r^{-3}}} = p^{{-15} - {(-15)}} \cdot r^{- {(-3)}} = r^{3}$.